Semi-linear degenerate backward stochastic partial differential equa- tions and associated forward backward stochastic differential equations

Authors

Kai Du, University of WollongongFollow
Qi Zhang, Fudan UniversityFollow

RIS ID

101363

Publication Details

Du, K. & Zhang, Q. (2013). Semi-linear degenerate backward stochastic partial differential equa- tions and associated forward backward stochastic differential equations. Stochastic Processes and their Applications, 123 (5), 1616-1637.

Abstract

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward-backward stochastic differential equations (FBSDEs) is established, which can be regarded as an extension of the Feynman-Kac formula to the non-Markovian framework.